In this paper, we show how wavelet analysis can be used to provide an efficient solution method for global illumination with glossy and diffuse reflections. Wavelets are used to sparsely represent radiance distribution functions and the transport operator. In contrast to previous wavelet methods (for radiosity), our algorithm transports light directly among wavelets, and eliminates the pushing and pulling procedures. The framework we describe supports curved surfaces and spatially-varying anisotropic BRDFs. We use importance to make the global illumination problem tractable for complex scenes, and a final gathering step to improve the visual quality of the solution.